Question

the responses of a sample of 5338 shoppers who were asked how their purchases are made are shown in the table. find the mean, the median, and the mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why.

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$$\begin{tabular}{|l|c|} \\hline \\textbf{how purchases are made} & \\textbf{frequency, f} \\\\ \\hline research online and in store, buy in store & 863 \\\\ search and buy online & 1050 \\\\ search and buy in store & 2255 \\\\ research online and in store, buy online & 1170 \\\\ \\hline \\end{tabular}$$

search and buy in store
research online and in store, buy online
search and buy online
research online and in store, buy in store
the data set does not have a mode.

does the mode represent a typical entry of the data? choose the correct answer below.
a. the mode represents a typical entry of the data set.
b. the mode does not represent the center because it is not a data entry.
c. the mode does not represent the center because it is the first data entry in the table.
d. the mode does not represent the center because it is the last data entry in the table.
e. the data set does not have a mode.

Explanation:

Identify the level of measurement and find the mode

The data represents qualitative (nominal) categories of how purchases are made. For nominal data, the mean and median cannot be calculated. The mode is the category with the highest frequency.

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Determine if the mode represents a typical entry

Since the data is nominal, the mode is the only measure of central tendency that can be identified, and it represents the most common (typical) response in the data set.

$$ \text{The mode represents a typical entry of the data set.} $$

Answer:

Question 1

• Search and buy in store (Correct answer)
• Research online and in store, buy online
• Search and buy online
• Research online and in store, buy in store
• The data set does not have a mode.

Question 2

• A. The mode represents a typical entry of the data set. (Correct answer)
• B. The mode does not represent the center because it is not a data entry.
• C. The mode does not represent the center because it is the first data entry in the table.
• D. The mode does not represent the center because it is the last data entry in the table.
• E. The data set does not have a mode.